
This notion is important because when the support of a coupling is \(c\) -cyclically monotone (henceforth referred to as \(c\) -CM), then it is optimal.
This relates to Theorem  because if there were a collection of points in the support that were not \(c\) -CM, then we could form a non-optimal measure via restriction.
The Kantorovich Duality Theorem, [1]}, is a standard result of the field, establishes the relationship between optimality and \(c\) -cyclic monotonicity as well as many other structural properties of optimal transport.
For our purposes, we focus on the equivalence between having \(c\) -CM support and optimality.
